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\title[Oral Defense]{Aggregate Economic Implications of New
  Technologies in Energy Industry}
\subtitle{Oral Defense}
\author{Xinya Zhang}
\institute{Department of Economics}

\date{April, 2013}

\begin{document}
\setcounter{tocdepth}{1}
\frame{\titlepage}

\begin{frame}
  \tableofcontents
\end{frame}

\section[Energy Sector Innovation and Growth]{Energy Sector Innovation and Growth: An Optimal Energy Crisis}
\begin{frame}{Introduction}
  \begin{itemize}
  \item A dynamic general equilibrium model
  \item Endogenous technological progress in energy production
  \item Technology innovation in the fossil fuel sector increases the
    supply of fossil fuel and allows fossil fuels to remain
    competitive for a longer period of time.
  \item A moving ``parity cost target'' for renewable energy
  \end{itemize}
\end{frame}

% \begin{frame}
%   \frametitle{Model Overview}
%   \begin{itemize}
%   \item Energy needed to produce the single good can come from
%     fossil fuel and renewables that are perfect substitutes
%   \item Fossil fuels currently are cheaper than renewables but costs
%     increase in the amount already extracted
%   \item  Although technological change in mining and energy use
%     can limit cost increases, depletion eventually raises cost
%     above the cost of renewables
%   \item  Learning by doing and explicit R\&D investment can then
%     reduce the costs of renewables once the switch occurs
%   \item An ``energy crisis" occurs when energy costs and energy
%     investments are at a maximum around the switch point
%   \end{itemize}
% \end{frame}


\subsection{The Macro Model}
\frame {
  \frametitle{The Model}
  {Goods and Service Production}
  \begin{itemize}
  \item Continuous time, single consumption good
  \item $c(t)$ is per capita consumption with utility
    \begin{equation}
      U = \max \int_{0}^{\infty }e^{-\beta \tau }\frac{c(\tau )^{1-\gamma }}{%
        1-\gamma }\,d\tau  \nonumber 
    \end{equation}
  \item Linear production function $y = Ak$
  \item Define units so $R + B = y$ where $R$ is per capita fossil fuel
    energy demand and $B$ is per capita renewable energy demand
  \item capital accumulation $\dot{k} = i-\delta k$
  \end{itemize}
}
\frame {
  \frametitle{Fossil fuel energy production}
  \vspace{1em}
  \begin{itemize}
  \item Population $Q$ grows at the constant rate
  \item Cumulative production $S$
    \begin{equation*}
      \dot{S} = QR 
    \end{equation*}
  \item  Since the low cost fields are exhausted first, per unit costs
    of fossil energy services $g(S,N)$ increase in $S$
  \item Increases in technical knowledge $N$ reduce $g(S,N)$ with
    fossil energy R\&D given by $n$
    \begin{equation*}
      \dot{N} = n
    \end{equation*}
  \end{itemize}
}
\frame
{
  \frametitle{Marginal cost of energy from fossil fuels}
  \begin{columns}
    \column{.6\textwidth}
    \begin{figure}[ht]
      \centering \includegraphics[width=3in]{ch1/MiningTC.pdf}
    \end{figure}
    \column{.4\textwidth}
    \begin{scriptsize}
      \begin{equation}
        \begin{split}
          g(S,N)&=\alpha _{0}+\frac{\alpha _{1}}{\bar{S}-S-\alpha _{2}/(\alpha _{3}+N)}%
          \\&=\alpha _{0}+\frac{\alpha _{1}(\alpha _{3}+N)}{(\bar{S}-S)(\alpha
            _{3}+N)-\alpha _{2}}
        \end{split}
        \notag
      \end{equation}
    \end{scriptsize}
  \end{columns}
}

\frame {
  \frametitle{  Renewable energy technology}
  \begin{itemize}
  \item Marginal cost $m$ of renewable energy services declines as
    new knowledge is gained
  \item A technological limit $\Gamma_2$, below which $m$ cannot fall
  \item H is the stock of technical knowledge in renewables
    \begin{equation*}
      m = 
      \begin{cases}
        (\Gamma _{1}+H)^{-\alpha } & \text{ if $H\leq \Gamma _{2}{}^{-1/\alpha }-$}
        \Gamma _{1}, \\  
        \: \Gamma _{2} & \text{otherwise}%
      \end{cases} 
    \end{equation*}
    
  \item Assume a two-factor learning model for $H$:
    \begin{equation*}
      \dot{H} = %
      \begin{cases}
        B^{\psi}j^{1-\psi} & \text{ if $H\leq \Gamma _{2}^{-1/\alpha }-$}\Gamma _{1}, \\ 
        0 & \text{otherwise}%
      \end{cases} 
    \end{equation*}
  \end{itemize} 
} 
\frame {
  \frametitle{  Optimization Problem}
  \begin{itemize}
  \item Resource Constraint:
    \begin{equation}
      c+i+j+n+g(S,N)R+pB = y=Ak  \nonumber
    \end{equation}
  \item Maximize the current value Hamiltonian and thus Lagrangian with respect to control
    variables $c$, $R$, $B$, $i$, $j$, and $n$.
    \begin{equation*}
      \begin{split}
        \mathcal{H}& =\frac{c^{1-\gamma }}{1-\gamma }+\lambda \left[
          Ak-c-i-j-n-g(S,N)R-(\Gamma _{1}+H)^{-\alpha }B\right] \\
        & +\epsilon (R+B-Ak)+q(i-\delta k)+\eta B(1+\psi j)+\sigma QR+\nu n+\mu j \\
        & +\omega n+\xi R+\zeta B+\chi \lbrack \text{$\Gamma _{2}^{-1/\alpha }-$}\Gamma _{1}-H]
      \end{split}
    \end{equation*}
  \item Initial conditions of state variables:
    \begin{equation*}
      S(0) = H(0) = N(0) = 0,\; k(0) = k_0 > 0
    \end{equation*}
  \end{itemize}
}
\frame {
  \frametitle{  Regimes of energy use and investment}
  \vspace{3em}
  \includegraphics[width = \textwidth]{/ch1/FourRegime.pdf}
}
\frame {
  \frametitle{Calibration}
  \begin{itemize}
  \item Assign numerical values to parameters so that the model is
    consistent with the actual world economy
    \vspace{1em}
  \item Data sources:
    \begin{itemize}
    \item Food And Agriculture Organization of the UN
    \item Energy Information Administration (EIA)
    \item Survey of Energy Resources, World Energy Council (WEC)
    \item Center for Global Trade Analysis, Purdue University (GTAP)
    \item Cambridge Energy Research Associates (CERA, 2009)
    \item National Energy Technology Laboratory (NETL)
    \item United States Geological Survey (USGS)
    \end{itemize}
  \end{itemize}
} 

\subsection{Results}
\frame {
  \frametitle{ Basic results}
  \begin{itemize}
  \item Transition to a renewable energy regime occurs after
    $T_1 = 88.41$ years
  \item Renewable energy is then used for a little more than 227
    years (until $T_2 = 315.8$) before $m$ attains its minimum
  \item Output per capita grows at an average annual rate of 4.22\%
    in the fossil regime, 3.11\% in the renewable regime with
    investment, and 4.07\% in the long run
  \end{itemize}
} 

\frame {
  \frametitle{ Fossil Regime Solutions}
  \begin{center}
    \includegraphics[ width=0.8\textwidth]{./ch1/ch1_fossil.pdf}
  \end{center}
}
\frame {
  \frametitle{ Fossil fuel cost functions}
  \begin{figure}[h]
    \centering
    \includegraphics[width = 0.8\textwidth]{ch1/g_functions.pdf}  
  \end{figure}

}

\frame {
  \frametitle{ Renewable regime solutions}
  \begin{center}
    \includegraphics[ width = 0.8\textwidth]{/ch1/ch1_renew.pdf}
  \end{center}
}

\frame {
  \frametitle{ An optimal energy crisis}

  The shadow price of energy remains more than double current values
  for over 75 years around the switch time. Consumption and output
  growth rates, and the share of consumption in output, all decline
  during this transition period. We thus identify the transition
  period as an ``energy crisis''.

  \begin{center}
    \includegraphics[width = \textwidth]{ch1/ch1_crisis.pdf}
  \end{center}
}
% \frame {
% \frametitle{Per capita consumption/output growth rate}
% \begin{columns}
%   \column{.6\textwidth}
%   \begin{figure}[ht]
%     \centering \includegraphics[width=3in]{ch1/GrowthRates.pdf}
%   \end{figure}
%   \column{.35\textwidth}
%   \begin{scriptsize}
%     \begin{itemize}
%     \item The economy starts with output and consumption growth
%       more or less equal
%     \item As the cost of fossil energy escalates, output growth
%       greatly exceeds consumption growth as more resources are
%       being plowed into maintaining energy supply
%     \item Per capita consumption growth drops substantially around
%       the ``energy crisis" and takes a very long time to recover
%       back to current levels
%     \item Output growth also plunges at the ``energy crisis" time
%     \item In the long run economy consumption growth equals
%       output growth
%     \end{itemize}
%   \end{scriptsize}
% \end{columns}
% }
%   \frame {
%   \frametitle{ Conclusions}
%   \begin{itemize}
%   \item The transition to renewables occurs at the end of this
%     century when about 80\% of available fossil fuels are gone
%   \item The energy shadow price peaks at the end of the fossil
%     regime and remains more than double current levels for
%     over 75 years around the switch time
%   \item While fossil energy costs are kept low for a long time, large
%     investments in energy technology are needed toward the
%     end of the fossil regime
%   \item Output shares of consumption and investment in $k$ decline
%   \item An ``energy crisis" occurs around the switch point, which is an effcient outcome in our economy
%   \item Learning-by-doing implies the economy will shift from
%     fossil to renewable energy prior to fossil fuels reaching the
%     parity cost of renewables.
%   \end{itemize}
% } 

\section[Competitive Equilibrium with Technological Externalities]{A Competitive Equilibrium
  Economy with Technological Externalities }

\begin{frame}
  \frametitle{Chapter 2}
  \tableofcontents[currentsection]
\end{frame}
\frame
{
  \frametitle{Competitive equilibrium model in discrete time}
  \begin{itemize}
  \item A representative household (consumer), a final good producer,
    a fossil energy producer, and a renewable energy producer.
  \item The household owns all factors of production and all shares in
    firms.
  \item In each period, the
    household sells factor services, extraction permits and technology patent to firms, buys goods, consumes some, and accumulates the rest as capital for the next period. 
  \item  Firms own nothing. They simply hire capital, energy input and  technology on a rental basis to produce output. They sell the output, and return all profits made to the shareholders.
  \end{itemize}
}

\frame
{
  \frametitle{}
  \begin{table}[h]
    \centering
    \begin{tabular}[h]{l l}
      \hline
      \hline
      \textbf{Symbol} & \textbf{Meaning} \\
      \hline
      $p_t$ & the price of a unit of final goods \\
      $r_t$ &  the price of capital\\
      $w_t$ &  the price of technology in fossil fuel sector\\
      $f_t$ &  the price of fossil fuel extraction permits \\
      $s_t$ &  the price of the knowledge patent on renewable energy\\
      $p_t^R$ & price of energy services from fossil fuel\\
      $p_t^B$ & price of energy services from  renewable  energy\\
      \hline
      \hline
    \end{tabular}
  \end{table}
  \underline{Final good producer's decision problem}
  \begin{align}
    \label{eq:finalProd}
    \max\pi^F &= \sum_{t=0}^{\infty }p_{t}\left[
      y_{t}^s-r_{t}k_{t}^{d}-p_{t}^{R}R_t^{d}-p_t^BB_t^d \right] \\
    \text{s.t. }y_{t} &\leq Ak_t \nonumber \\
    y_t &= R_t + B_t  \nonumber
  \end{align}
}
\frame
{
  \frametitle{Fossil fuel energy producer's problem}

  \begin{align}
    \label{eq:fossilProd}
    \max\pi ^{R} = &\sum_{t=0}^{\infty }p_{t}\left[
      p_{t}^{R}R_{t}^{s}-g(S_{t}^d,N_{t}^d)R_{t}^{s}-w_tN_t^d+f_tS_t-f_tS_{t+1})
    \right] \\
    \text{s.t. } &S_{t+1} = S_{t}+Q_{t}R_{t} \nonumber\\
    &Q_{t+1} = (1+\pi)Q_t \nonumber\\
    &g(S_{t},N_{t}) =
    \alpha_0+\frac{\alpha_1}{\bar{S}-S_t-\frac{\alpha_2}{\alpha_3+N_t}} \nonumber\\
    & S_0\text{, } Q_0 \text{ is given} \nonumber
  \end{align}

}

\frame
{
  \frametitle{Renewable energy producer's  problem}
  \begin{align}
    \label{eq:renewProd}
    \max\pi ^{B} &= \sum_{t=0}^{\infty }p_{t}
    \left[ p_{t}^{B}B_{t}^{s}-m_{t}B_t^s-s_tH_t+s_tH_{t+1})\right]  \\
    \text{s.t. } &m_{t} =
    \begin{cases}
      &(\Gamma _{1}+H_{t})^{-\alpha },\quad
      \text{if }H\leq \Gamma _{2}{}^{-1/\alpha}-\Gamma _{1}, \\
      &\Gamma _{2}, \quad  \text{otherwise}
    \end{cases} \nonumber\\
    & H_{t+1} = H_{t}+
    \begin{cases}
      &B_{t}^{\psi }j_{t}^{1-\psi },\quad
      \text{if } H_{t}\leq \Gamma _{2}^{-1/\alpha}-\Gamma _{1}, \\
      &0, \quad \text{otherwise.} \nonumber
    \end{cases} \\
    &H_0 \text{ is given} \nonumber
  \end{align}
}

\frame
{\frametitle{Representative Household's problem}
  \begin{align}
    \label{eq:household}
    \max&\sum_{t=0}^{\infty }\beta ^{t}\frac{c_{t}^{1-\gamma }}{1-\gamma } \\
    \text{s.t. }\sum_{t=0}^{\infty }p_{t}\left(
      c_{t}+i_{t}+n_{t}+j_{t}\right)
    &\leq \sum_{t=0}^{\infty }p_{t}\big[
    r_{t}k_{t}+w_tN_t+s_t(H_t-H_{t+1}) \nonumber \\
    &+f_t(S_{t+1}-S_t)\big] +\pi +\pi^{R}+\pi ^{B}  \notag \\
    k_{t+1} &= (1-\delta )k_{t}+i_{t} \notag \\
    N_{t+1} &=  N_{t}+n_{t} \notag \\
    H_{t+1} &= H_{t}+
    \begin{cases}
      B_{t}^{\psi }j_{t}^{1-\psi } &
      \text{if} H_{t}\leq \Gamma _{2}^{-1/\alpha}-\Gamma _{1}, \\
      0 & \text{otherwise.} \nonumber
    \end{cases} \\
    & k_0\text{, } N_0 \text{, and } H_0 \text{ is given.} \nonumber
  \end{align}
}


\frame
{
  \frametitle{A Competitive Equilibrium is}
  A set of prices $ \{(p_{t},r_{t},w_t, s_t, f_t,
  p_{t}^{R},p_{t}^{B})\}_{t=0}^{\infty}$,\\
  An allocation $ \{(c_t, i_t, n_t, j_t, k_{t+1}, N_{t+1}, S_{t+1},
  H_{t+1}, k_t^s, N_t^s, S_t^s, H_t^s)\}_{t=0}^{\infty} $,
  for the household, \\
  An allocation
  $\{(y_{t},k_{t}^{d},R_{t}^{d},B_{t}^{d})\}_{t=0}^{\infty}$ for
  the final
  good producer, \\
  An allocation $\{(N_t^d, S_t^d, S_{t+1},
  R_{t}^{s})\}_{t=0}^{\infty}$ for the  fossil fuel producer, \\
  An allocation $\{(H_{t}^d, B_{t}^{s}, H_{t+1})\}_{t=0}^{\infty}$
  for the renewable energy producer, such that, at the
  stated price,

  \begin{enumerate}
  \item $\{(y_{t},k_{t}^{d},R_{t}^{d},B_{t}^{d})\}_{t=0}^{\infty }$
    solves problem \eqref{eq:finalProd};
  \item $\{(N_t^d, S_t^d, S_{t+1}, R_{t}^{s})\}_{t=0}^{\infty}$ solves problem
    \eqref{eq:fossilProd};
  \item $\{(H_t^d, B_{t}^{s}, H_{t+1})\}_{t=0}^{\infty }$ solves problem \eqref{eq:renewProd};
  \item $\{(c_t, i_t, n_t, j_t, k_{t+1}, N_{t+1}, S_{t+1}, H_{t+1}, k_t^s,
    N_t^s, S_t^s, H_t^s)\}_{t=0}^{\infty}$ solves problem \eqref{eq:household};
  \item Markets clear in all periods.
  \end{enumerate}
}
\frame
{
  \frametitle{Find the Competitive Equilibrium}
  \begin{itemize}
  \item Zero profits for firms: $\pi^F = \pi^R = \pi^B$
  \item $p_t^R = g(S_t,N_t) + f_tQ_t$
  \item $p_t^B = m_t - \psi s_tB_t^{\psi-1}j_t^{1-\psi}$
  \item At $p_t^R = p_t^B$, economy transits from fossil fuel to renewable energy
  \item Benefits of learning by doing make it worthwhile to transit before the energy cost parity
  \end{itemize}
}

\subsection{Pareto Optimal Results}
% \frame
% {
%   \frametitle{Basic results}
%   \begin{itemize}
%   \item Transition to a renewable energy regime occurs after $T_{1}=98$ years when over 75\% of available fossil fuels are gone.
%   \item Renewable energy is then used for a little more than 221 years (until $T_{2}=308$) before marginal cost $q$ attains its minimum
%   \item Output per capita grows at an average annual rate of 4.36\% in the fossil regime, 3.13\% in the renewable regime with investment, and 4.07\% in the long run
%   \end{itemize}
% }
\frame
{
  \frametitle{Fossil fuel regime solutions}
  \begin{figure}[h]
    \centering \includegraphics[width=3in]{ch2/full_logPO.pdf}
\caption{$T_{1}=98$ years, $S_{T_1}$ = 1595, $T_2 = 366$ years}
  \end{figure}
}
%\frame
% {
%   \frametitle{Renewable regime solutions}
%   \begin{figure}[h]
%     \centering \includegraphics[width=4in]{ch2/renew2PO.pdf}

%   \end{figure}
% }
\subsection{Technological Externalities}
\frame
{
  \frametitle{ Knowledge Spillover}
  \begin{itemize}
  \item  Let $\bar{B}_{t}$, $\bar{j}_{t}$ stand for the aggregate levels of $B$
    and $j$, respectively
    \begin{align*}
      H_{t+1}=H_{t}+
      \begin{cases}
        (\bar{B}_{t}^{\theta}\bar{j}_{t}^{\rho})B_{t}^{\psi-\theta }j_{t}^{1-\psi-\rho } & \text{ if $
          H_{t}\leq \Gamma _{2}^{-1/\alpha }-$}\Gamma _{1}, \\
        0 & \text{otherwise}
      \end{cases}
    \end{align*}
  \item $\theta$: the spillover weight of learning by doing
\item $\rho$: the spillover weight of R\&D investment
    \end{itemize}
\begin{table}
  \begin{tabular}[h!]{c c c c c}
    \hline
    \hline
Case & A & B & C & D \\
    & $\rho = 0$, & $\rho = 0.05\psi$, & $\rho = 0.25\psi$, & $\rho = 0.95\psi$,  \\
Variables & $\theta = 0$ &  $\theta = 0.95\psi$  & $\theta = 0.75\psi$ & $\theta = 0.95\psi$ \\
\hline
$T_2$ & 366 & 387 & 400 & 436\\
$T_1$ & 98 & 103 & 106 & 112 \\
$S_{T_1}$ & 1595 & 1582 & 1579 & 1570\\
\hline
\hline 
 \end{tabular}
  \centering
  \end{table}
}
\frame
{
  \frametitle{Comparison: Fossil Fuel Regime}
  \begin{figure}[ht]
    \centering \includegraphics[width=3.5in]{ch2/fossil1.pdf}
  \end{figure}
}

\frame
{
  \frametitle{Comparison: Fossil fuel regime-continued}
  \begin{figure}[ht]
    \centering \includegraphics[width=3.5in]{ch2/fossil2.pdf}
  \end{figure}
}
\frame
{
  \frametitle{Comparison: Renewable energy regime}
  \begin{figure}[ht]
    \centering \includegraphics[width=3.5in]{ch2/renew1.pdf}
  \end{figure}
}
\frame
{
  \frametitle{Conclusion}
\begin{enumerate}
\item Knowledge spillovers lead to sub-optimal solutions: lower
investment in R\&D, slower technological progress, and lower
output and consumption.  
\item With knowledge spillovers, the fossil fuel regime of the economy lasts a longer time but with less fossil fuels consumed. The economy also experiences higher energy prices during the transition period.
\item R\&D spillovers (case D) appear to lead to the most severe under-investment problem and retard the economy the most.
\end{enumerate}
}

% \frame
% {
%   \frametitle{Results and future work}
%   \textbf{Results} \\
%   \begin{itemize}
%   \item Due to lower investment in R\&D, economy takes longer to reach the technological frontier (about 10 years).  
%   \item Fossil fuel regime ends 2 years early with less fossil fuel consumed
%   \item Goods price is higher all along the time, while lower fossil fuel price and higher renewable price have been detected
%   \end{itemize}
%   \vspace{1em}
%   \textbf{Future work}
%   \begin{itemize}
%   \item policy variables 
%   \item Environment externalities  or energy
%     independence issues
%   \end{itemize}
% } 
\section[Case Study of Job Creation in the Shale and the Wind Industries]{Local Employment Impacts of Competing Energy Sources: the Case of Shale Gas Production and Wind Generation in Texas}
\begin{frame}
  \frametitle{Chapter 3}
  \tableofcontents[currentsection]
\end{frame}
\subsection{Introduction}
\frame{
  \frametitle{Motivation}
  \begin{itemize}
  \item An extensive ongoing policy discussion on renewable energy 
  \item Wind is the fastest growing source of renewable generation
  \item Shale oil and gas revolution has been taken place at the same time 
\item Estimate number of jobs created by these two competing resources 
  \end{itemize}
}
\frame {
  \frametitle{Fast growing wind and natural gas generation}
  \begin{figure}[ht]
    \centering \includegraphics[width=3.7in]{ch3/summercap.pdf}
    \caption{Electricity net summer capacity by source, 1949-2011}
  \end{figure}
}

% \frame
% {
%   \frametitle{Installed Wind Capacity in U.S}
%   \begin{columns}
%     \column{0.6\textwidth}
%     \begin{figure}[ht]
%       \centering \includegraphics[width=4in]{ch3/windprod.jpg}
%       \label{fig:windprod}
%     \end{figure}
%     \column{0.3\textwidth}
%     % \begin{scriptsize}
%     %   Wind energy accounted
%     %   for about 75\% of newly installed U.S. renewable electricity capacity
%     %   in 2011 while electricity generation from biomass, geothermal, and
%     %   hydropower have remained relatively stable since 2000
%     % \end{scriptsize}
%   \end{columns}
% }
% \frame
% {
%   \frametitle{Shale Production in U.S}
%   \begin{columns}
%     \column{0.6\textwidth}
%     \begin{figure}[ht]
%       \centering \includegraphics[width=3in]{ch3/shaleprod.jpg}
%       \label{fig:shaleprod}
%     \end{figure}
%     \column{0.3\textwidth}
%     \begin{scriptsize}
%       Shale oil and gas revolution has been taking place, and has led to economic revitalization and job creation in places like Texas, North Dakota, West Pennsylvania, Louisiana, etc
%     \end{scriptsize}
%   \end{columns}
% }
\frame{
  \frametitle{Literature}
  \begin{itemize}
   \item (UTSA2012): Eagle Ford, 14-County Region in 2011: 38001 full
    time jobs
  \item (IHS2010): The shale gas industry supported 600,000 jobs in
    2010.
  \item (AWEA2012):The entire wind energy sector directly and
    indirectly employed 75,000 full-time workers at the end of 2011.
  \item Gulf Wind Project: 283.2 MW, 250-300 jobs during peak construction period, 15 - 20 permanent jobs.
  \item (NRDC2012): One typical wind farm of 250MW would create 1079
    jobs over the lifetime of the project.
  \end{itemize}
}
\subsection{Data description}
\frame{
  \frametitle{Data Description}
\begin{itemize}
\item Balanced panel with N = 254 county observations in Texas and T =
  132 months in 11 years from 2001 to 2011
  
\item Employment and wage data: Quarterly Census of
    Employment and Wages (QCEW) Database of the Bureau of Labor
    Statistics (BLS)
\item Well completion dates and located counties: Drilling Info Database
   \item Installed capacity and online date:
    {\it American Wind Energy Association} (AWEA)
  \item Wind farm location: wind projects' websites 
\end{itemize}
}

\frame{
  \frametitle{Variables}
   For counties i = 1, ..., 254 and months t = 1, ..., 132, the variables are:
  \begin{enumerate}
  \item Total employment in all industries: emp$_ {it}$
  \item Real weekly average wage (adjusted by GDP deflator from BEA): wage$_ {it}$
  \item Number of wells completed(directional, fractured; by completion date): wells$_ {it}$
  \item Cumulative number of wells completed: cumuwells$_ {it}$
  \item New installed wind capacity added (in MW): newcap$_ {it}$
  \item Cumulative installed wind capacity (in MW): cumucap$_ {it}$
  \end{enumerate}
}

\frame{
  \frametitle{Distribution of wells and wind capacity}
  \begin{itemize}
    \item 31,050 wells completed in 174 counties during 2001 - 2011
    \item 125 wind projects, 10006 MW wind capacity, has installed in 41 counties during 2001 - 2011
  \end{itemize}
\begin{figure}[h]
\centering
\subfloat[]{\includegraphics[width=0.5\textwidth]{ch3/wells.pdf}}
\subfloat[]{\includegraphics[width=0.5\textwidth]{ch3/windcap.pdf}}
\end{figure}
}
\frame{
  \frametitle{Data Properties}
  \begin{itemize}
  \item Stationarity: ADF(LLC/IPS) tests and KPSS/Hadri tests  
    \begin{itemize}
    \item 135 counties have stationary employment series.
    \item 145 counties have stationary realwage series.
    \item $wells$ and $wcap$ are stationary. 
    \end{itemize}
  \item Arbitrary dependence between $x_{it}$ and $c_i$
  \item Strict Exogeneity conditional on $c_i$: $E(u_{it}|\mathbf{x}_i,c_i) = 0, t = 1,2,...,T$ 
  \item Serial correlation: could be eliminated by including lagged variables or mechanistically fixing with robust covariance matrix or FGLS method. 
  \end{itemize}    
}

\frame{
  \frametitle{Autoregressive Distributed Lag Model}
  We start with a general ADL model and test down to a more
  specific model, including the optimal values for $p$ and $q$.
\begin{align}
  \label{eq:ADL} {E}_{it} &=\sum_{j=1}^p\lambda_j E_{i,t-j} +
\sum_{k=0}^q\beta_k{wells}_{i,t-k} +
\sum_{k=0}^q\delta_k{wcap}_{i,t-k} + c_i + \theta_t + u_{it}
\end{align}  
\begin{itemize}
\item $p = 2$, $q = 19$: Two way fixed effects
\item Long-run propensity(LRP) = $\frac{\sum_{k=0}^{19}\hat{\beta_k}}{1-\hat{\lambda_1}-\hat{\lambda_2}}$ = 121.13
\item $p = 0$, $q = 19$: First difference feasible GLS 
\item LRP = ${\sum_{k=0}^{19}\tilde{\beta_k}}$ = 121.69 
  \end{itemize}

}

\frame{
  \frametitle{Results}
  \begin{columns}
    \column{0.5\textwidth}
    \begin{scriptsize}
      Impact on Employment
      \begin{itemize}
      \item 121 long term jobs can be created per well completion
      \item Given that 5482 new directional/fractured wells were completed in Texas in 2011, 663,322 new full-time jobs were created 
      \item Wind impact on employment is not significant from zero. 
      \end{itemize}
    \end{scriptsize}
    \column{0.5\textwidth}
    \begin{scriptsize}
      Impact on Wage
      \begin{itemize}
      \item  Long term weekly average wage will increase by 33 cents per well completion
      \item Since the average weekly wage is \$576, it will increase about 0.6\% if 10 wells are drilled
      \item  Wind impact on employment is not significant from zero.
      \end{itemize}
    \end{scriptsize}  
  \end{columns}

}

\frame{
  \frametitle{Spatial Interaction Effects}
  \begin{itemize}
  \item Spatial interactions could be due to competition between counties, spillovers, externalities,regional correlations in industry structures, etc
  \item 254*254 spatial weights matrix $W$:
    \begin{align*}
      w_{ij} = 
      \begin{cases}
        1, \text{ if $i$ and $j$ are neighbors}, i\neq j\\
        0, \text{ otherwise}
      \end{cases}
    \end{align*}
  \item Then transform $W$ into row-standardized form, which assumes 
    the impact on each unit by all other units are equal
  \end{itemize}
}

\frame{
  \frametitle{Spatial Panel Data Models}
   \begin{align*}
  E_{it} &= \rho\sum_{j=1}^N w_{ij}E_{jt} + \beta_1{wells}_{it} + \beta_2{wcap}_{it} + u_{it} \\
    &u_{it} = \lambda\sum_{j=1}^N w_{ij}u_{jt} + \epsilon_{it} \\
  &\epsilon_{it} = c_i + \nu_{it}
\end{align*}
\begin{itemize}
\item Spatial lag model(SAR): $\lambda = 0$
\item Spatial error model(SEM): $\rho = 0$

\end{itemize}

  
}

\frame{
  \frametitle{Spatial interaction effects on employment}
  \begin{table}[h]
   \centering
   \begin{tabular}{|l|c|c|c|c|}  
     \hline
\multicolumn{5}{|l|}{SAR Coefficients:}\\
\hline
      & Estimate &Std. Error &t-value &Pr$(>|t|)$\\
\hline
$\rho$ &0.1730 &0.0081 &21.43   &$<2e-16^{***}$\\
wells  &224.72 &12.99 &17.29   &$<2e-16^{***}$\\
newcap &0.05 &6.366 &0.0079   &0.9937    \\
\hline
\multicolumn{5}{|l|}{SEM Coefficients:} \\
\hline    
$\lambda$   & 0.1734 &0.0081 &21.42   &$<2e-16^{***}$\\
wells  &235.81 &13.63 &17.30   &$<2e-16^{***}$\\
newcap &0.47 &6.374  &0.704   &0.4814   \\
\hline 
\multicolumn{5}{|l|}{Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 } \\
\hline
  \end{tabular}
\end{table}
}

\frame{
  \frametitle{Spatial panel results}
  \begin{itemize}
  \item the expectation of the SAR model $y = \rho Wy +X\beta+\epsilon$ is
\begin{align*}
  E(y) &= (I_N-\rho W)^{-1}X\beta \\
  \partial y/\partial x_r' &= (I_N-\rho W)^{-1}I_N\beta_r 
\end{align*}
\item The average total effects of well drilling activity on employment are 271, in which 225 from direct effects and 46 from indirect effects.
\item The direct and indirect effects of well drilling activity on wage are 0.18 and 0.06, respectively. Hence, total effect on wage is 23 cents.
\item The effects of wind activity are  not statistically significant.
 \end{itemize}
}

\frame{
\frametitle{}
\begin{center}
\textbf{Questions....\\
\& \\
Thank you!}
\end{center}
}
\end{document}
